On 4/14/10 11:34 AM, Lin Xie wrote:
> Hi, Leo
> Thanks for the reply! Well, the integral is a problem in modelling
> microdomain structures in crystal and to my knowledge I do not know
> that the problem can be easily overcomed in such way.
Why not? Aren't you trying to integrate over R^n?
The matrix A can be easily determined from your expression. If E is the
the quadratic, then the matrix A that Leo refers to is
genmatrix(lambda([i,j], if i = j 1 else
coeff(coeff(E,concat(x,j)),concat(x,i))),8,8)
I have forgotten exactly what the result of the integration would be,
but the determinant of A in this case is not too complicated:
factor(ratsimp(determinant(A))) ->
(t-r+1)^2*(t+r+1)^2*(t-2*s+r+1)*(t+2*s-r+1)*(3*t-2*s-r-1)*(3*t+2*s+r-1)
(It's not clear to me if this expression positive or not.)
Ray